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Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, January 30, 2004

16:28
Math competition question 

There's a big math competition coming up next week and two of the Algebra II questions had my mentor teachers stumped. One was a problem that I've already seen: x+y=35, xy=7, what is 1/x+1/y? It's actually a kind of standard brain-teaser question (hint: you don't need to find the value of x or y. If you follow the link to the older diary entry, you'll find the answer.

The second is similar in spirit, but a bit harder. We're given two quadratic equations with integer coefficients: ax2+bx+c=0 has its largest root 2, and ax2+cx+b=0 has its largest root 3. The greatest common denominator of a, b and c is 1. What is b+c? I've not yet worked this one out. My instinct is that we would solve this as a linear diophantine equation, but that seems a bit much to expect of Algebra II students. More in the comments to spare those who want to try working it out on their own.

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